Singularity-rank signatures in generalized Dirac oscillators near a BTZ black-hole horizon

The near-horizon behavior of a Dirac field depends on both the black-hole geometry and the radial structure of its interactions. We investigate this dependence for singular generalized Dirac-oscillator couplings near a nonextremal BTZ black-hole horizon. The proper acceleration of stationary observers corotating with the horizon and its radial gradient motivate inverse-radial and inverse-square interactions. An exact stationary spin frame yields the finite contribution H Ω Ω H to the rotating radial coupling. The inverse-radial system is Fuchsian and admits an exact Whittaker solution; its equivalent componentwise confluent-Heun representation contains an apparent finite singularity. The inverse-square system is irregular, with essential factors e± β ₂/ρρ -1/2 e ± β 2 / ρ ρ - 1 / 2 . From the Riccati equation for the finite-radius spinor response, we derive a large-damping expansion and connect it to the selected near-horizon branch. For the two power-law profiles matched in value at the comparison radius, their different radial slopes first distinguish the real responses at order γ ⁻² γ - 2 for nonzero rotation and at order γ ⁻³ γ - 3 in the nonrotating limit. Numerical integration supports the predicted asymptotic scaling and quantifies the geometric truncation error for the sampled parameters. The local solutions provide finite-radius matching data for the full exterior spectral problem.